SOLUTION: if one leg of a right triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs..

Algebra ->  Pythagorean-theorem -> SOLUTION: if one leg of a right triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs..      Log On


   

Question 341496: if one leg of a right triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs..
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
if one leg of a right triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs.
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Let one of the legs have length x.
Then the other leg's length is x-14.
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Using Pythagoras you get:
26^2 = x^2 + (x-14)^2
x^2 + x^2-28x+196 = 676
2x^2 -28x -480 = 0
x^2 -14x -240 = 0
(x-24)(x+10) = 0
Positive solution:
x = 24 meters (longer leg)
x-14 = 10 meters (shorter leg)
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Cheers,
Stan H.